Lower bounds of the slope of fibred threefolds

Details Lower bounds of the slope of fibred threefolds Lower bounds of the slope of fibred threefolds

1999-09-14

arxiv.org/abs/math/9909073v1

Mathematics

Algebraic Geometry

34 pages

Scientific paper

We study from a geographical point of view fibrations of threefolds over smooth curves, such that the general fibre is of general type. We prove the non-negativity of certain relative invariants under general hypotheses and give lower bounds for the self-interssection of the relative canonical divisor of the fibration, depending on other relative invariants. We also study the influence of the relative irregularity on these bounds. A more detailed study of the lowest cases of the bounds is given.

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